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MeganDarling

  • 2 years ago

A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins

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  1. jim_thompson5910
    • 2 years ago
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    Start off by defining variables

  2. jim_thompson5910
    • 2 years ago
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    let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)

  3. MeganDarling
    • 2 years ago
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    okey (:

  4. jim_thompson5910
    • 2 years ago
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    If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?

  5. MeganDarling
    • 2 years ago
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    That they add up to 11 pounds haha

  6. jim_thompson5910
    • 2 years ago
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    good, so x y and z add to 11, which means x+y+z = 11

  7. jim_thompson5910
    • 2 years ago
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    that's one equation

  8. MeganDarling
    • 2 years ago
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    so x+y+z=11 :o

  9. jim_thompson5910
    • 2 years ago
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    yes

  10. MeganDarling
    • 2 years ago
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    But then we have to factor in how much they cost..

  11. jim_thompson5910
    • 2 years ago
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    We also know that "The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars

  12. jim_thompson5910
    • 2 years ago
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    this total cost is given to be $21 so 1.5x + 3y + 1.5z = 21

  13. MeganDarling
    • 2 years ago
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    so like, 1.50x+3.00y+1.50=21..

  14. MeganDarling
    • 2 years ago
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    Haha Okey you already said that x.x my bad

  15. MeganDarling
    • 2 years ago
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    1.50z* I meant btw haha. I get that indeed.

  16. jim_thompson5910
    • 2 years ago
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    close, you mean to say 1.50x+3.00y+1.50z=21 but you got it

  17. MeganDarling
    • 2 years ago
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    And don't forget twice the peanuts!

  18. jim_thompson5910
    • 2 years ago
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    that's your 2nd equation

  19. jim_thompson5910
    • 2 years ago
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    twice the peanuts as what?

  20. MeganDarling
    • 2 years ago
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    it says, the recipe calls for twice as many peanuts as almonds O.o

  21. jim_thompson5910
    • 2 years ago
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    good, so the equation for that is?

  22. MeganDarling
    • 2 years ago
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    ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.

  23. jim_thompson5910
    • 2 years ago
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    not quite

  24. MeganDarling
    • 2 years ago
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    knew it was wrong x.x

  25. jim_thompson5910
    • 2 years ago
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    Amount of peanuts = 2 times (amount of almonds)

  26. jim_thompson5910
    • 2 years ago
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    y = 2 times x or just y = 2x

  27. MeganDarling
    • 2 years ago
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    oh pshh I should have thought of that x.x

  28. jim_thompson5910
    • 2 years ago
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    so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x

  29. jim_thompson5910
    • 2 years ago
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    you can use them to solve for x, y and z

  30. jim_thompson5910
    • 2 years ago
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    I'll get you started

  31. MeganDarling
    • 2 years ago
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    Lol I can't because I'm stupid, But smart people definitely can haha

  32. jim_thompson5910
    • 2 years ago
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    x+y+z = 11 x+2x+z = 11 3x+z = 11 --------------------- 1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21

  33. jim_thompson5910
    • 2 years ago
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    so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21

  34. MeganDarling
    • 2 years ago
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    O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me

  35. jim_thompson5910
    • 2 years ago
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    where are you lost?

  36. jim_thompson5910
    • 2 years ago
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    I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11

  37. jim_thompson5910
    • 2 years ago
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    I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21

  38. MeganDarling
    • 2 years ago
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    oh okay ! I see now, sorry it's really late and I'm super tired :/

  39. jim_thompson5910
    • 2 years ago
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    so you have 3x+z = 11 7.5x + 1.5z = 21 now

  40. jim_thompson5910
    • 2 years ago
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    solve the first equation for z to get this 3x+z = 11 3x+z - 3x = 11 - 3x z = 11 - 3x

  41. MeganDarling
    • 2 years ago
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    Alrighty

  42. jim_thompson5910
    • 2 years ago
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    Since z = 11 - 3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11 - 3x) = 21 Solve for x

  43. jim_thompson5910
    • 2 years ago
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    oh wait, i made a variable mistake...i switched x and y one sec

  44. jim_thompson5910
    • 2 years ago
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    Let me fix real quick

  45. MeganDarling
    • 2 years ago
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    I was thinking that haha x) ..

  46. MeganDarling
    • 2 years ago
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    uhh ? your comment disappeared .. :o

  47. jim_thompson5910
    • 2 years ago
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    it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11 - 3y --------------------------- 1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11 - 3y) = 21 Solve that last equation for y

  48. jim_thompson5910
    • 2 years ago
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    sry

  49. jim_thompson5910
    • 2 years ago
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    Solve 6y + 1.5(11 - 3y) = 21 for y

  50. MeganDarling
    • 2 years ago
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    haha it's okay

  51. MeganDarling
    • 2 years ago
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    Aw man I have to go to bed soon I'm dead tired x.x

  52. jim_thompson5910
    • 2 years ago
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    What do you get when you solve that equation for y

  53. MeganDarling
    • 2 years ago
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    ergh I dunno x.x I'm brain dead

  54. jim_thompson5910
    • 2 years ago
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    Then give it a break, get some sleep and you'll tackle it in the morning

  55. MeganDarling
    • 2 years ago
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    Oh no I keep losing connection >.<

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